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Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers
Double U-pipe boreholes are the second most used type of ground heat exchangers after single U-pipe boreholes. The borehole thermal resistance is a key design and performance parameter for the double U-pipe boreholes. Another parameter that is particularly important for double U-pipe boreholes is the internal thermal resistance between the U-pipes. There is, however, a general lack of methods that can be used to calculate the thermal resistances of the double U-pipe boreholes. This article presents explicit multipole formulas for calculating thermal resistances of double U-pipe boreholes with symmetrically positioned pipes. The presented formulas include zeroth- and first-order expressions for the borehole thermal resistance and the internal thermal resistance. The internal thermal resistance formulas cover various possible flow configurations of the heat carrier fluid in the double U-pipes. The accuracy of the presented zeroth- and first-order formulas is established by comparing them to the original 10th-order multipole method. The article also presents thermal network models for computing effective borehole thermal resistance of double U-pipe boreholes from the multipole resistances. Formulas for calculating effective borehole thermal resistance of double U-pipe boreholes are presented for two idealized cases of uniform heat flux and uniform average wall temperature along the borehole.
Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers
Double U-pipe boreholes are the second most used type of ground heat exchangers after single U-pipe boreholes. The borehole thermal resistance is a key design and performance parameter for the double U-pipe boreholes. Another parameter that is particularly important for double U-pipe boreholes is the internal thermal resistance between the U-pipes. There is, however, a general lack of methods that can be used to calculate the thermal resistances of the double U-pipe boreholes. This article presents explicit multipole formulas for calculating thermal resistances of double U-pipe boreholes with symmetrically positioned pipes. The presented formulas include zeroth- and first-order expressions for the borehole thermal resistance and the internal thermal resistance. The internal thermal resistance formulas cover various possible flow configurations of the heat carrier fluid in the double U-pipes. The accuracy of the presented zeroth- and first-order formulas is established by comparing them to the original 10th-order multipole method. The article also presents thermal network models for computing effective borehole thermal resistance of double U-pipe boreholes from the multipole resistances. Formulas for calculating effective borehole thermal resistance of double U-pipe boreholes are presented for two idealized cases of uniform heat flux and uniform average wall temperature along the borehole.
Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers
Claesson, Johan (author) / Javed, Saqib (author)
Science and Technology for the Built Environment ; 25 ; 980-992
2019-09-14
13 pages
Article (Journal)
Electronic Resource
English
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